Syntonic–chromatic equivalence continuum: Difference between revisions
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Created page with "The '''syntonic-chromatic equivalence continuum''' is a continuum of temperaments which equate a number of syntonic commas (81/80) with the 2187/2048|chromatic sem..." |
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All temperaments in the continuum satisfies (81/80)<sup>''n''</sup> ~ 2187/2048. Varying ''n'' results in different temperaments such as [[whitewood]], [[mavila]], [[dicot]], [[porcupine]], [[tetracot]], [[amity]], [[gravity]], and [[absurdity]]. It converges to [[meantone]] as ''n'' approaches infinity. The just value of ''n'' is 5.2861… | All temperaments in the continuum satisfies (81/80)<sup>''n''</sup> ~ 2187/2048. Varying ''n'' results in different temperaments such as [[whitewood]], [[mavila]], [[dicot]], [[porcupine]], [[tetracot]], [[amity]], [[gravity]], and [[absurdity]]. It converges to [[meantone]] as ''n'' approaches infinity. The just value of ''n'' is 5.2861… | ||
{| class="wikitable center- | {| class="wikitable center-1 center-2" | ||
|+ Temperaments in the continuum | |+ Temperaments in the continuum | ||
|- | |- | ||
! ''n'' | ! rowspan="2" | ''n'' | ||
! Temperament | ! rowspan="2" | Temperament | ||
! Comma | ! colspan="2" | Comma | ||
|- | |||
! Ratio | |||
! Monzo | |||
|- | |- | ||
| 0 | | 0 | ||
| [[Whitewood]] | | [[Whitewood]] | ||
| [[2187/2048]] | | [[2187/2048]] | ||
| {{monzo| -11 7 }} | |||
|- | |- | ||
| 1 | | 1 | ||
| [[Mavila]] | | [[Mavila]] | ||
| [[135/128]] | | [[135/128]] | ||
| {{monzo| -7 3 1 }} | |||
|- | |- | ||
| 2 | | 2 | ||
| [[Dicot]] | | [[Dicot]] | ||
| [[25/24]] | | [[25/24]] | ||
| {{monzo| -3 -1 2 }} | |||
|- | |- | ||
| 3 | | 3 | ||
| [[Porcupine]] | | [[Porcupine]] | ||
| [[250/243]] | | [[250/243]] | ||
| {{monzo| 1 -5 3 }} | |||
|- | |- | ||
| 4 | | 4 | ||
| [[Tetracot]] | | [[Tetracot]] | ||
| [[20000/19683]] | | [[20000/19683]] | ||
| {{monzo| 5 -9 4 }} | |||
|- | |- | ||
| 5 | | 5 | ||
| [[Amity]] | | [[Amity]] | ||
| [[1600000/1594323]] | | [[1600000/1594323]] | ||
| {{monzo| 9 -13 5 }} | |||
|- | |- | ||
| 6 | | 6 | ||
| [[Gravity]] | | [[Gravity]] | ||
| 129140163/128000000 | | [[129140163/128000000]] | ||
| {{monzo| 13 -17 6 }} | |||
|- | |- | ||
| 7 | | 7 | ||
| [[Absurdity]] | |[[Absurdity]] | ||
| 10460353203/10240000000 | | 10460353203/10240000000 | ||
| {{monzo| 17 -21 7 }} | |||
|- | |- | ||
| … | |||
| … | | … | ||
| … | | … | ||
| Line 49: | Line 61: | ||
| [[Meantone]] | | [[Meantone]] | ||
| [[81/80]] | | [[81/80]] | ||
| {{monzo| -4 4 -1 }} | |||
|} | |} | ||
[[Category:Theory]] | [[Category:Theory]] | ||
[[Category:Temperament]] | [[Category:Temperament]] | ||
Revision as of 03:51, 7 December 2020
The syntonic-chromatic equivalence continuum is a continuum of temperaments which equate a number of syntonic commas (81/80) with the chromatic semitone (2187/2048).
All temperaments in the continuum satisfies (81/80)n ~ 2187/2048. Varying n results in different temperaments such as whitewood, mavila, dicot, porcupine, tetracot, amity, gravity, and absurdity. It converges to meantone as n approaches infinity. The just value of n is 5.2861…
| n | Temperament | Comma | |
|---|---|---|---|
| Ratio | Monzo | ||
| 0 | Whitewood | 2187/2048 | [-11 7⟩ |
| 1 | Mavila | 135/128 | [-7 3 1⟩ |
| 2 | Dicot | 25/24 | [-3 -1 2⟩ |
| 3 | Porcupine | 250/243 | [1 -5 3⟩ |
| 4 | Tetracot | 20000/19683 | [5 -9 4⟩ |
| 5 | Amity | 1600000/1594323 | [9 -13 5⟩ |
| 6 | Gravity | 129140163/128000000 | [13 -17 6⟩ |
| 7 | Absurdity | 10460353203/10240000000 | [17 -21 7⟩ |
| … | … | … | … |
| Inf | Meantone | 81/80 | [-4 4 -1⟩ |